A lot depends on the size of your plot, Kevin. if you have room, you could plant a tree which will take up some of the water. The most important thing before you start is to improve the soil with compost and perhaps dig in some good, bought topsoil. If water really is a problem, you could also dig a drainage trench and fill it with stones. Much will also depend on the aspect of your plot (north, south ,east or west) and whether it is in sun or shade. If the soil is just wet because you live in a rainy area, clay will dry out in better weather to be hard and solid, brick-like in fact. This is where the dug-in compost comes in; it changes the texture of the soil to help it drain better and make it easier to dig and plant. Clay soil is usually pretty fertile. Here is another point: if you live in a new house, the soil in your garden may not be topsoil at all, but the clay subsoil dug up by the builders. It will be a funny, grey-beige colour and look unpleasant and congealed. If your soil is like this, you will need to replace it with topsoil.

Sorry if this is condescending and tells you things you know, but you haven't left much information.

I have an area of soil like this Kevin. It will be saturated now but come summer it will split open with cracks big enough to fall in. Ribes is doing well. Bamboo not bad. Physocarpus 'Diablo' died, winter honeysuckle and climbing hydrangea struggle. Nothing small stands a chance against the cracks. I think it would take more compost than I can produce to alter it. I'm thinking of trying some of the red stemmed dogwoods but they may not manage the summer.

Plants suck water in the growing season but the soil gets dry and you've still got saturation in winter. Those that like the saturation in the winter complain in the summer. Difficult. I'm still working on it.